An Entropy Method for Diversified Fuzzy Portfolio Selection

This paper proposes an entropy method for diversified fuzzy portfolio selection. Proportion entropy is introduced and credibilistic mean-variance and mean-semivariance diversification models for fuzzy portfolio selection are proposed. The crisp forms of the proposed models are also provided when the security returns are all triangular fuzzy variables. As an illustration, an application example of mean-variance diversification model is given using real data from Shanghai Stock Exchange. The computation results show that the proposed model results in a more diversified investment than the credibilistic mean-variance model.

[1]  George C. Philippatos,et al.  Entropy, market risk, and the selection of efficient portfolios , 1972 .

[2]  John M. Cozzolino,et al.  The Maximum-Entropy Distribution of the Future Market Price of a Stock , 1973, Oper. Res..

[3]  George C. Philippatos,et al.  Conditions of Equivalence Among E-V, SSD, and E-H Portfolio Selection Criteria: The Case for Uniform, Normal and Lognormal Distributions , 1975 .

[4]  David N. Nawrocki,et al.  State-value weighted entropy as a measure of investment risk , 1986 .

[5]  J. N. Kapur.  Maximum-entropy models in science and engineering , 1992 .

[6]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[7]  Arun J. Prakash,et al.  Portfolio selection and skewness: Evidence from international stock markets , 1997 .

[8]  S. Fang,et al.  Entropy Optimization and Mathematical Programming , 1997 .

[9]  Yian-Kui Liu,et al.  Expected value of fuzzy variable and fuzzy expected value models , 2002, IEEE Trans. Fuzzy Syst..

[10]  Maria Rosaria Simonelli.  Indeterminacy in portfolio selection , 2005, Eur. J. Oper. Res..

[11]  A. Yu. Popkov,et al.  Entropy model of the investment portfolio , 2006 .

[12]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[13]  Amelia Bilbao-Terol,et al.  Fuzzy compromise programming for portfolio selection , 2006, Appl. Math. Comput..

[14]  P. Jana,et al.  Multi-objective Mean-variance-skewness model for Portfolio Optimization , 2007 .

[15]  Xiaoxia Huang.  Portfolio selection with fuzzy returns , 2007, J. Intell. Fuzzy Syst..

[16]  C. R. Bector,et al.  A subjective assessment of approximate probabilities with a portfolio application , 2007 .

[17]  Xiaoxia Huang,et al.  Mean-semivariance models for fuzzy portfolio selection , 2008 .

[18]  Xiaoxia Huang,et al.  Mean-Entropy Models for Fuzzy Portfolio Selection , 2008, IEEE Transactions on Fuzzy Systems.

[19]  Baoding Liu,et al.  Entropy of Credibility Distributions for Fuzzy Variables , 2008, IEEE Transactions on Fuzzy Systems.

[20]  Pankaj Gupta,et al.  Asset portfolio optimization using fuzzy mathematical programming , 2008, Inf. Sci..

[21]  Zhongfeng Qin,et al.  Portfolio selection based on fuzzy cross-entropy , 2009 .

[22]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[23]  Robert Malouf.  Maximum Entropy Models , 2010 .

[24]  Wilhelm Rödder,et al.  An entropy-driven expert system shell applied to portfolio selection , 2010, Expert Syst. Appl..

[25]  Xiaoxia Huang,et al.  Portfolio Analysis - From Probabilistic to Credibilistic and Uncertain Approaches , 2012, Studies in Fuzziness and Soft Computing.

[26]  Desheng Dash Wu,et al.  Portfolio selection using λ mean and hybrid entropy , 2011, Ann. Oper. Res..

[27]  Yeliz Mert Kantar,et al.  Mean-Variance-Skewness-Entropy Measures: A Multi-Objective Approach for Portfolio Selection , 2011, Entropy.

[28]  Weijun Xu,et al.  An optimization model of the portfolio adjusting problem with fuzzy return and a SMO algorithm , 2011, Expert Syst. Appl..

[29]  Samarjit Kar,et al.  Fuzzy mean-variance-skewness portfolio selection models by interval analysis , 2011, Comput. Math. Appl..

[30]  Harry M. Markowitz,et al.  Mean‐Variance Model for Portfolio Selection , 2012 .